node wrangler while editing a group
With the node wrangler addon &#9096; Ctrl&#8679; Shift LMB connects the node to the material output node and adds an emission shader if the node output is not a shader. The material output node shouldn't be used inside a node group so node wrangler does not make that shortcut active when editing a node group.

You should have the material output node in the material node tree and connect the group output to the material output node, not have the material output node inside a node group.

It is not possible to make a connection from a node inside a group to the active material output node that is outside the group. As connecting the node to the group output does not guarantee that the output will then be connected to the material output and the group could be in use by several materials, it makes little sense to use it inside a node group.